题目
A garden centre sells bags of stones and large bags of gravel. The weight, X kilograms, of stones in a bag can be modelled by a normal distribution with unknown mean and known standard deviation 0.4 The stones in each of a random sample of 36 bags from a large batch is weighed. The total weight of stones in these 36 bags is found to be 806.4 kg
(a) Find a 98% confidence interval for the mean weight of stones in the batch.
(b) Explain why the use of the Central Limit theorem is not required to answer part (a)
The manufacturer of these bags of stones claims that bags in this batch have a mean weight of 22.5 kg
(c) Using your answer to part (a), comment on the claim made by the manufacturer.
The weight, Y kilograms, of gravel in a large bag can be modelled by a normal distribution with mean 850 kg and standard deviation 5 kg A builder purchases 10 large bags of gravel.
(d) Find the probability that the mean weight of gravel in the 10 large bags is less than 848 kg
题目中文翻译
一家园艺中心出售装石子的袋子和装大颗粒砾石的袋子。 袋中石子的重量 千克可由一个正态分布建模，其均值未知为 ，已知标准差为 0.4。 从一大批货物中随机抽取 36 袋并称重。 这 36 袋石子的总重量为 806.4 千克。
(a) 求这批石子平均重量的 98% 置信区间。
(b) 解释为什么解答 (a) 小题时不需要使用中心极限定理。
制造商声称，这批袋子中的平均重量为 22.5 千克。
(c) 利用 (a) 小题的答案，对制造商的说法作出评论。
一袋大颗粒砾石的重量 千克可由正态分布建模，其均值为 850 千克，标准差为 5 千克。 一位建筑工人购买了 10 袋大颗粒砾石。
(d) 求这 10 袋砾石平均重量小于 848 千克的概率。